Normal and conormal maps in homotopy theory

Details Normal and conormal maps in homotopy theory Normal and conormal maps in homotopy theory

2010-11-25

arxiv.org/abs/1011.5597v2

Mathematics

Algebraic Topology

32 pages. The definition of twisting structure in Appendix B has been reformulated, leading to further slight modifications of

Scientific paper

Let M be a monoidal category endowed with a distinguished class of weak equivalences and with appropriately compatible classifying bundles for monoids and comonoids. We define and study homotopy-invariant notions of normality for maps of monoids and of conormality for maps of comonoids in M. These notions generalize both principal bundles and crossed modules and are preserved by nice enough monoidal functors, such as the normaliized chain complex functor. We provide several explicit classes of examples of homotopy-normal and of homotopy-conormal maps, when M is the category of simplicial sets or the category of chain complexes over a commutative ring.

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